Topography of molecular scalar fields. II. An appraisal of the hierarchy principle for electron momentum densities

Abstract

The previously observed hierarchy principle for nondegenerate critical points (CPs) of the electron momentum density (EMD) of molecules [ Kulkarni, Gadre, and Pathak, Phys. Rev. A. 45, 4399 (1992) ] is verified at a reliable level of theory. Application of Morse inequalities and the Poincaré-Hopf relation to EMD leads to some rigorous results viz (i) for total number of CPs, N_CP = 3,7,11,15,... there must be either a (3,+3) or a (3,-1) CP at the center of symmetry, (ii) for N_CP = 1,5,9,13,... there must be either a (3,-3) or a (3,+1) CP at the center of symmetry. A single directional maximum on every ray, starting from p = 0 has been observed for all the test molecules and is suggested as a working topographical principle in p space. This working principle is shown to satisfy the sufficiency condition for the hierarchy principle.